The following correction was printed in the Guardian's Corrections and clarifications column, Tuesday August 5 2008

In our account of an interview, conducted in English and in Japanese through a translator, with members of the Yellow Magic Orchestra, keyboardist Ryuichi Sakamoto was quoted in a way which may have implied that he found the presence of black people at a filming of the Soul Train TV show in Hollywood in 1980 "intimidating". Sakamoto denies having said this, and our interviewer confirms there was nothing in their conversation that could have suggested that Sakamoto held racist views.

December 1980. America's premier black music show, Soul Train, is being filmed in Hollywood. The crowd is dancing to the soul hits of the day - Stevie Wonder's Master Blaster, Kool & the Gang's Celebration, Donna Summer's The Wanderer - and singing along with the ballad Ooh Baby by Tower of Power crooner Lenny Williams.

Then veteran host Don Cornelius introduces three rather nerdy Japanese men called YMO - or Yellow Magic Orchestra. "It was the turn of the crazy Japanese guys," laughs Haruomi "Harry" Hosono, YMO's bassist. "We performed our song Computer Games, and everyone went mad."

"They were breakdancing and bodypopping," says the band's drummer and lead singer, Yukihiro Takahashi. "We'd never seen anything like it."

"It was quite intimidating," says keyboardist Ryuichi Sakamoto. "Everyone else on the show was black. The audience was black. The crew and the presenters were black. There were no white or Asian faces there. Suddenly, it was the Oriental guys who were being asked to make the dance music, which defied every stereotype!"

Between 1978 and 1984, they went on to confound stereotypes. Hip-hop pioneer Afrika Bambaataa, who sampled their music, was only half-joking when he said that Yellow Magic Orchestra invented hip-hop. Their singles Firecracker and Tighten Up were both big R&B hits in the US, while Computer Games became a top 20 UK hit, earning them the adoration of synth pop acts such as Ultravox, John Foxx, Gary Numan and Duran Duran. Over the next three decades, their influence cropped up in odd areas: producer Todd Rundgren had a YMO album on the wall of his studio for inspiration; Eric Clapton's unlikely cover version of YMO's Behind the Mask was a huge international hit; while the arcade-game bleeps and oriental scales in their music went on to influence 21st-century electronica acts such as Dizzee Rascal and Kieran Hebden, who weren't even born when YMO were formed. Meanwhile, in Japan, they were bigger than the Beatles.

"We were very big," sighs Sakamoto, "that's why I hated it. We were always followed by paparazzi."

"Yes, and teenage girls," says Hosono. "They would literally chase us down the street and rip our clothes to shreds."

"I quite enjoyed that," says Takahashi.

In Europe, however, the audience response was often rather more cerebral.

"In Italy, the audience would start arguing during our concert," says Hosono. "You had these very serious-looking men with beards and long hair, having a symposium about our music while we were playing."

"They looked like Greek or Roman philosophers," says Sakamoto. "It was so funny."

It's a few days before their historic reunion show at the Royal Festival Hall - their first UK date since 1980 - where they have been asked to play by Meltdown curators Massive Attack. The three YMO members - grey-haired and astonishingly dapper - are sitting in the bar of their Pimlico hotel, and all of them seem to conform to stereotype: Hosono (61) is the amusingly grumpy, de facto band leader; Takahashi (56) is the rakish design student, wearing an immaculately tailored mod suit and a pork-pie hat; while Sakamoto (56) is the handsome, floppy-fringed intellectual, wearing sharp, modernist, designer threads.

They have long been heralded as godfathers of techno, part of a pioneering wave of musicians who brought synthesiser technology into the charts. However, unlike their peers in Sheffield or Basildon, these weren't untutored, one-fingered soloists, but experienced musicians. In the early 1970s, Hosono led an exotica band called Happy End, which explored country and western and Hawaiian music; Takahashi played in a glam rock outfit called the Sadistic Mika Band, who'd toured the UK with Roxy Music (and even appeared on the Old Grey Whistle Test and Pebble Mill at One, where they were interviewed by a baffled Jan Leeming), while Sakamoto was a classically trained session musician.

Furthermore, while their peers in Düsseldorf and Detroit were using synthesiser technology to create a bleak, dystopian vision of the future - a world of faceless robots and brutal post-industrial landscapes - the YMO saw technology as something joyous and liberating. In their hands, the synthesiser was a cuddly, slightly whimsical instrument.

"I think that's a Japanese thing," says Sakamoto. "Japan used to be an animistic society before Shinto imperialism was established. But most of us still have an animistic sense. And you can see it in the way in which we use tools. For us, those tools are not just objects. Japanese people can feel some attachment in what they are making, whether it is a car or a TV or a computer. It's like when Sony made that pet robotic dog. From the beginning, nobody in Japan had any fear or apprehension about that. Even old people thought it was cute."

Hosono and Sakamoto in particular were always obsessed with Japanese cultural identity. The band's name is a sly joke at Japan's obsession with black magic ("yellow magic was halfway between white magic and black magic," says Hosono. "Actually, it's a stupid name, isn't it?"), and the band constantly explored notions of Asianness, exoticisation and orientalism. Their first single, for instance, was a version of Martin Denny's "oriental" anthem Firecracker from a defiantly Japanese perspective.

'The thing was to take these western ideas of the exotic, but to subvert them," says Hosono. "With Martin Denny, the exotica is kind of fake. But I am real! I am the target of that western exotica. So what I wanted to make was exotica from an oriental perspective."

All three maintained solo careers even during YMO's peak. "By that last year, I think we started pursuing our solo careers rather more vigorously," laughs Yukihuro.

Sakamoto, always the heartthrob of the band, had the highest international profile, collaborating first with David Sylvian and XTC's Andy Partridge, before going on to work with artists as diverse as David Byrne, Iggy Pop and Talvin Singh. He wrote operas, soundtracks for Hollywood movies (The Last Emperor), and even starred in one (Merry Christmas Mr Lawrence). Hosono and Yukihuro continued to make music in Japan, and to collaborate as a duo called Sketch Show. After a chance meeting with Sakamoto at Barcelona's Sonar festival in 2004, they tentatively started collaborating as a trio. They played at Tokyo's Live Earth festival in 2007, and began writing and recording material.

"Now we are too old and weary to fight," laughs Sakamoto. "And it is fun to work together again."

"And it is so much easier now," says Hosono. "In the old days, our synthesizers had no memory function. When we played live, it was a nightmare. As we were playing one song, we had a computer programmer backstage, tapping out the computer code for the next song."

"And, if it was taking him longer than usual," says Takahashi, "we'd have to take longer solos."

"Now we can just press a few buttons, and everything is set up for the next song," says Sakamoto. "Japanese technology is very good, isn't it?"